Related papers: Interpretations of Linear Orderings in Presburger …
Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…
This paper gives a decision procedure for the validity of en- tailment of symbolic heaps in separation logic with Presburger arithmetic and arrays. The correctness of the decision procedure is proved under the condition that sizes of arrays…
Abstract numeration systems encode natural numbers using radix ordered words of an infinite regular language and linear recurrence sequences play a key role in their valuation. Sequence automata, which are deterministic finite automata with…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
Word equations are a crucial element in the theoretical foundation of constraint solving over strings. A word equation relates two words over string variables and constants. Its solution amounts to a function mapping variables to constant…
We show that if A is a linear order then Th(A) is either $\aleph_0$-categorical or Borel complete (in the sense of Friedman and Stanley). We generalize this; if A has countably many unary predicates attached, then Th(A) is…
A wide variety of model explanation approaches have been proposed in recent years, all guided by very different rationales and heuristics. In this paper, we take a new route and cast interpretability as a statistical inference problem. We…
This paper studies tree-automatic ordinals (or equivalently, well-founded linearly ordered sets) together with the ordinal addition operation +. Informally, these are ordinals such that their elements are coded by finite trees for which the…
We study notions of generic and coarse computability in the context of computable structure theory. Our notions are stratified by the $\Sigma_\beta$ hierarchy. We focus on linear orderings. We show that at the $\Sigma_1$ level all linear…
Tasks that model the relation between pairs of tokens in a string are a vital part of understanding natural language. Such tasks, in general, require exhaustive pair-wise comparisons of tokens, thus having a quadratic runtime complexity in…
This paper initiates the reverse mathematics of social choice theory, studying Arrow's impossibility theorem and related results including Fishburn's possibility theorem and the Kirman--Sondermann theorem within the framework of reverse…
We often desire our models to be interpretable as well as accurate. Prior work on optimizing models for interpretability has relied on easy-to-quantify proxies for interpretability, such as sparsity or the number of operations required. In…
We identify difference-bound set constraints (DBS), an analogy of difference-bound arithmetic constraints for sets. DBS can express not only set constraints but also arithmetic constraints over set elements. We integrate DBS into separation…
Interpretations are a fundamental tool in mathematical logic, allowing structures to be encoded within other structures via logical definitions. We study $\MSO$ \emph{multidimensional point interpretations}, where elements of an interpreted…
We investigate finite deterministic automata in sets with non-homogeneous atoms: integers with successor. As there are uncount- ably many deterministic finite automata in this setting, we restrict our attention to automata with semilinear…
We consider the problem of counting the number of answers to a first-order formula on a finite structure. We present and study an extension of first-order logic in which algorithms for this counting problem can be naturally and conveniently…
In this article, we develop a new and somewhat unexpected connection between higher-order model-checking and linear logic. Our starting point is the observation that once embedded in the relational semantics of linear logic, the Church…
Generalized numberings are an extension of Ershov's notion of numbering, based on partial combinatory algebra (pca) instead of the natural numbers. We study various algebraic properties of generalized numberings, relating properties of the…
This paper proposes a new framework for learning a rule ensemble model that is both accurate and interpretable. A rule ensemble is an interpretable model based on the linear combination of weighted rules. In practice, we often face the…
The theory of classical realizability is a framework in which we can develop the proof-program correspondence. Using this framework, we show how to transform into programs the proofs in classical analysis with dependent choice and the…